On Two Classes of Test Matrices

摘要

Two classes of matrices which are useful in testing numerical algorithms for problems in linear algebra are presented. Their determinants, eigenvalues, eigenvectors and inverses are deduced in analytic forms. These are easily generated by machine or by hand as functions of certain parameters in the original matrices. By appropriately selecting the parameters one is able to generate ill-conditioned matrices without having to deal with high order matrices. (Author)